It all started with orange hot pants, white go-go boots and lots of cocktails.

In the late Sixties, when Rollin King, the owner of a small Texan air commuter service, sat down with Herb Kelleher, a lawyer in the same southern US state, little did they know that a plan sketched out on a napkin would later trigger a global revolution in air travel.

The pair had an idea for a new airline that would shuttle passengers between the Texan cities of Houston, Dallas and San Antonio for fares as low as $20 one-way.

That brainstorming session over drinks resulted in the creation in 1967 of Air Southwest, a small inter-state carrier that was renamed Southwest Airlines and launched its inaugural flight on June 18, 1971.

Southwest started a format that was later replicated by copy-cats around the world, with its quirky, headline-grabbing branding. Leggy air hostesses in hot pants and white boots sashayed down the aisles of its Boeing 737-200s serving cocktails and free peanuts.

In a television advertisement from 1972, one hostess boasted: “Remember what it was like before Southwest Airlines? You didn’t have hostesses in hot pants.”

It may have raised a few eyebrows at the time, but Southwest’s theme for its cabin crew of “long legs, short nights” was a hit with Americans looking to travel for less.

The stellar growth of the pioneering new airline over the next two decades also caught the attention of several aspiring aviation executives across the Atlantic.

Two men in particular saw the genius in Southwest’s low fares and no-frills model: Michael O’Leary and Stelios Haji-Ioannou.

In 1990, Ryanair, a small airline set up five years previously by Ireland’s wealthy Ryan family, was making losses of £20m. Its founder, Tony Ryan, was desperate to save the carrier, which began with one route between Waterford in south-east Ireland and London Gatwick but had grown rapidly in the late Eighties.

O’Leary, a former accountant at KPMG, had originally recommended closing the carrier, but was dispatched by Ryan to Texas to see how the Americans made it work.

He came back inspired and Ryanair, which had business class seats and a frequent flyer club, was reborn as a low-cost carrier offering passengers cheap, no-frills flights to secondary airports in Europe.

A few years later, a young Stelios was also keen to start a similar shake-up in UK aviation.

Born in a cramped office at Luton Airport shared with the airport’s spectators’ club, easyJet started its assault on the UK market by advertising flights to Edinburgh and Glasgow that were “as cheap as a pair of jeans”.

Now that same airline flies 60.5m passengers a year on more than 612 routes across 30 countries.

But as we approach the end of 2013, a new mood is in town. O’Leary has admitted that his resolutely no-frills approach at Ryanair may have run its course.

And Carolyn McCall, chief executive at easyJet, has had a stellar run boosted by “speedy boarding”, more flexible fares, guaranteed seats and better food.

Last week, at The Telegraph’s Festival of Business (FoB), Willie Walsh, the chief executive of International Airlines Group, owner of British Airways and Iberia, said a chapter in low-cost air travel was coming to a close. It’s been quite a journey.

Walsh was at Ireland’s legacy carrier, Aer Lingus, during a period of particularly meteoric growth for the low-cost airlines.

When he became chief executive of Aer Lingus in 2001, its low-cost rival Ryanair was transporting 9.4m passengers a year. By the time he left to become chief executive of British Airways in 2005, Ryanair’s passenger figures had more than tripled to 34.8m.

Walsh admitted at the FoB that most national flag-carriers simply underestimated their budget rivals.

At the turn of the last decade, when many of the legacy airlines were bending beneath the weight of their high cost-bases and were struggling to recover from the shock of 9/11, Walsh asked a team at Aer Lingus to see how they could cut down the time needed to turn aircraft around at an airport from 45 minutes to the 25 minutes achieved by Ryanair.

The team divided itself into three, with one group looking at how to board passengers faster, the second at what happens during the turnaround, and the third at how to disembark customers quicker.

“It was a fantastic presentation until I pointed out to them that they hadn’t stitched it together, so they had people boarding the aircraft before all of the passengers were off the aircraft,” Mr Walsh recalled with a laugh.

Instead, Aer Lingus was reduced to espionage to work out how its competitor executed turnarounds in such a short time. It hid a camera on an airport stand and spied on Ryanair.

“We recorded Ryanair for a day. They turned the aircraft around in exactly the same way every time,” said Walsh, who believes the key to Ryanair’s success has been its simplicity.

Lufthansa’s former chairman, Jürgen Weber, also learned the hard way that Ryanair’s disruptive business model and its outspoken chief executive were not to be dismissed lightly.

When the Irish budget carrier first broke into the German market, Lufthansa dismissed its new rival, claiming German passengers wouldn’t like budget fares. O’Leary’s characteristically colourful retort generated reams of free newspaper coverage for the new brand and its cheap fares.

The success of Ryanair in Germany sparked the airline to place what was at the time the largest ever aircraft order by an Irish airline to accommodate German passengers who flocked, the airline claimed, “in their millions”.

Over the past 15 years, although the low-cost sector has not been immune from failure – for example, Flyglobespan and Zoom – budget airlines have profitably snatched 40pc of intra-Europe air travel revenues, according to analysts at Barclays. This has been possible because low-cost airlines have a unit cost advantage on the flag-carriers of around 35pc.

Barclays estimates that revenues in the European low-cost carrier industry have expanded by a compound annual growth rate of 21pc over the past decade.

But after 10 years of gaining altitude at such a rapid pace, warning bells rang out in September when Ryanair shocked the markets with its first profit warning in a decade. The caution was quickly followed by a second just two months later, as the carrier said intense competition in the European short-haul market had pushed down fares over the winter.

O’Leary, who has in the past called customers “stupid” for not turning up to airports with their boarding passes already printed, launched a charm offensive. Ryanair is simplifying its website – previously a major bugbear for many passengers, who were forced to go through 17 “clicks” before they could make their booking.

The airline is also rolling out other initiatives that mark a major departure from its no-frills roots, such as allocated seating. It is a change that has proved highly successful at easyJet, which ended the free-for-all at its boarding gates last year.

IAG’s Walsh believes that the European airline industry is now entering what is going to be “the most exciting period in the history of the industry”.

“We are going to witness a lot of change that will be positive from an industry point of view and you are going to see the emergence of the winners and the losers quite clearly over the next five years,” he said.

Winter can be a fight for survival for airlines, and Walsh believes the industry will see more legacy airlines, which are currently operating on life support, failing.

While that offers an opportunity for budget carriers to snatch even more market share, the “duopoly” shared by Ryanair and easyJet in the low- cost market is also being challenged by a group of ambitious, entrepreneurial airlines such as Norwegian Air Shuttle, Vueling, which is owned by IAG, Wizz Air and Pegasus, of Turkey.

Andrew Lobbenberg, airlines analyst at HSBC, agrees that the next few years are likely to herald significant changes in the European market.

“We have seen a trend over the past 10 years of the flag-carriers, the charter airlines and the regional airlines all ceding market share to low-cost airlines. There is little reason to expect that over-arching trend to change,” he says.

“But the nature of the competition within the sector is certainly changing. What we have seen in the last five to 10 years is very many start-up low-cost airlines and the overwhelming majority of them have failed and disappeared.

“Where we are now, through a process of Darwinism, those that have survived in the shadow of the towering two leaders are not bad and they are now pushing on because they see the scale of the opportunity and they want some of it. It’s a really fluid environment.”

Norwegian has been making waves in Scandinavia since it started operating flights on the west coast of Norway in 1993 but the carrier, led by former fighter pilot Bjørn Kjos, has ambitions far beyond its heartland and has gradually been encroaching on territory previously dominated by easyJet and Ryanair.

The airline, which is also launching budget transatlantic flights from the UK, last year placed one of Europe’s biggest aircraft orders, buying 222 narrow-body jets to fuel its short-haul ambitions on the continent.

In the summer, IAG also ordered 62 new narrow-body jets for Vueling, which currently has a fleet of 70 aircraft, and Walsh has not been shy about his ambitions for the Barcelona-based carrier, which he claims has a more efficient cost base than easyJet and a “more friendly service culture” than Ryanair.

With certain legacy carriers such as Alitalia fighting for survival and others such as Iberia cutting back on capacity, analysts are gearing up for a dogfight over the skies of Europe as both the incumbent low- cost airlines and the younger challengers jostle to pick up some of the potential prizes on offer.

“It’s going to be a potentially significant winter,” says Douglas McNeill, investment director at Charles Stanley Direct. “Winter is the time when seasonal cash flow is at its weakest, so it’s always a challenge for certain weaker airlines to get through the winter – Alitalia is the most obvious case.”

Some believe that Ryanair’s recent downgrade in profits was a tactical move by O’Leary that will allow him to embark on a price war and stamp out some of the new competition from the likes of Norwegian. Analysts will this week press easyJet on current trading conditions and whether the airline will have to lower prices to fight off rivals.

While it has been working hard to encourage more repeat customers, easyJet is taking the competition seriously, according to insiders, although it believes some of its more ambitious rivals will struggle to gain enough take-off and landing slots at capacity-constrained airports such as Gatwick, Paris Orly and Milan Malpensa to grow rapidly in key markets.

During the summer, easyJet dominated 41pc of peak take-off and landing slots at Gatwick between 6am and 8.55am. The next biggest slot owner was BA, with 17pc, and other carriers such as Monarch, Norwegian and Flybe had 4pc, 6pc and 8pc respectively.

So while some in the City believe O’Leary has taken his eye off the ball by failing to spot the demand for better customer service earlier, few believe easyJet and Ryanair’s duopoly in European short-haul faces a serious threat.

Surprisingly, easyJet and Ryanair together still account for only 20pc of the overall European short-haul market, according to Investec, highlighting a significant opportunity to snatch more share from embattled flag-carriers.

“Ryanair is such a phenomenal operator that it would take a staggering level of turnaround for them not to do well,” says James Hollins, of Investec.

“They have been this cheeky chappy front-runner of the low-cost movement in Europe. Now they are using that scale to say: ‘Actually, we can do more to create a better product’.”

Hollins believes easyJet’s move to allocated seating last year has been a “game-changer” for the airline.

Since taking the helm of easyJet in 2010, McCall has made a concerted effort to move the airline that became famous for its bright orange livery away from its original budget branding and ensure that it is seen as a credible alternative to the legacy carriers, while still maintaining a low cost-base.

As it only flies to primary airports in Europe and therefore only competes with Ryanair on fewer than 5pc of its routes, easyJet has told investors that it believes it can compete for an additional 86m seats at the top 20 airports where it operates if more passengers can be persuaded that low fares don’t mean poor service.

It has calculated that it has a 22pc share of capacity at those leading airports, which include Gatwick, but flag-carriers still account for 53pc.

But with the new touchy-feely Ryanair also making significant improvements to turn its flights into a more pleasurable experience, is the budget model in danger of disappearing altogether?

The model is undoubtedly moving upmarket, says Lobbenberg, of HSBC. “Their business model is absolutely evolving, but you go and buy a cheap car today – a cheap Skoda or something.

“Compare that car with what a cheap car was 20 years ago, or 10 years ago, it was probably a Skoda then but the Skodas now don’t look the same as they did. Yes, the products are evolving upmarket but that’s not anything that is necessarily unique to airlines.”

Following years of low-cost airlines’ pranks and gimmicks, McNeill, of Charles Stanley Direct, believes Ryanair and easyJet have simply matured.

“Budget carriers are no longer upstart challengers to the status quo, they are establishment now. They have learned and are learning to operate like mature companies.”

Long legs and short nights are a long way in the past.

Ready for take-off: A short history of low-cost

1971

Southwest Airlines, the inspiration for many low cost airlines in Europe, launches its first flights, between the Texan cities of Houston, Dallas and San Antonio.

1985

Ryanair launches its first flight, from Waterford in south-east Ireland to Gatwick. The crew had to be shorter than 5ft 2in to fit in the cabin.

1990

Ryanair’s founders, the Ryan family, inject £20m into the airline, which had racked up losses of £20m, and re-launch it as a low cost operator based on Southwest US.

1995

Stelios Haji-Ioannou founds easyJet in a small office at Luton Airport, which was shared with the local airline spectators club

1998

British Airways creates Go to compete with the new low cost carriers but admits it ended up cannibalising its own business. Go is sold two years later and is eventually acquired by easyJet

2012

EasyJet makes a significant move away from its no frills roots by rolling out allocated seating across its network.